Ring (mathematics) — This article is about algebraic structures. For geometric rings, see Annulus (mathematics). For the set theory concept, see Ring of sets. Polynomials, represented here by curves, form a ring under addition and multiplication. In mathematics, a… … Wikipedia
Jacobson radical — In ring theory, a branch of abstract algebra, the Jacobson radical of a ring R is an ideal of R which contains those elements of R which in a sense are close to zero . DefinitionThe Jacobson radical is denoted by J( R ) and can be defined in the… … Wikipedia
Jacobson-Radikal — In der Ringtheorie, einem Zweig der Algebra, bezeichnet das Jacobson Radikal eines Rings R ein Ideal von R, das Elemente von R enthält, die man als „nahe an Null“ betrachten kann. Das Jacobson Radikal ist nach Nathan Jacobson benannt, der es als… … Deutsch Wikipedia
Ring theory — In abstract algebra, ring theory is the study of rings algebraic structures in which addition and multiplication are defined and have similar properties to those familiar from the integers. Ring theory studies the structure of rings, their… … Wikipedia
Jacobson density theorem — In mathematics, the Jacobson density theorem in ring theory is an important generalization of the Artin Wedderburn theorem. It is named for Nathan Jacobson.It states that given any irreducible module M for a ring R , R is dense in its bicommutant … Wikipedia
Nathan Jacobson — Nathan Jacobson, 1974 Nathan Jacobson (October 5, 1910, Warsaw, Congress Poland, Russian Empire December 5, 1999, Hamden, Connecticut) was an American mathematician.[1] Born in Warsaw, Jacobson emigrated to America with his Jewish family in 1918 … Wikipedia
Glossary of ring theory — Ring theory is the branch of mathematics in which rings are studied: that is, structures supporting both an addition and a multiplication operation. This is a glossary of some terms of the subject. Contents 1 Definition of a ring 2 Types of… … Wikipedia
Semiprimitive ring — In mathematics, especially in the area of algebra known as ring theory, a semiprimitive ring is a type of ring more general than a semisimple ring, but where simple modules still provide enough information about the ring. Important rings such as… … Wikipedia
Noncommutative ring — In mathematics, more specifically modern algebra and ring theory, a noncommutative ring is a ring whose multiplication is not commutative; that is, if R is a noncommutative ring, there exists a and b in R with a·b ≠ b·a, and conversely.… … Wikipedia
Local ring — In abstract algebra, more particularly in ring theory, local rings are certain rings that are comparatively simple, and serve to describe what is called local behaviour , in the sense of functions defined on varieties or manifolds, or of… … Wikipedia
